One paratrooper was shot dead by a sniper in the ruins of Donetsk's international airport, where Ukrainian forces are almost surrounded by rebels, the military said in a statement.
Another 15 servicemen were wounded as government positions around the conflict zone came under repeated bombardment, the statement said.
The deadly fighting rumbled on in the industrial east despite a two-month old ceasefire deal that has halted significant offensives, but failed to stop shelling at strategic flashpoints along the frontline.
Over 4,000 people -- mostly civilians -- have been killed in the conflict since April, the United Nations said.